The authors can cast the cause-effect pair problem as a regular machine learning classification problem in which input-output pairs $( P_{Π = π} ( X , Y )$, G = g ) are drawn randomly and independently from a $\textbf{“mother distribution” }$ $P_M( P_{Π = π} ( X , Y ), G = g )$, then divided into training and test sets.

The problem is to “classify” distributions $P_{Π = π} ( X , Y )$ into one of four classes $g ∈ \{ X → Y , X ← Y , X \leftrightarrow Y , X ⊥ Y \}$